President of the Eurogroup Jeroen Dijsselbloem, told a news conference: "Possible cases have to be discussed and assessed on their own merits, once the instrument enters into force."

EU ministers gave no guarantee that an Irish application would be successful in securing ESM assistance. There is also no indication as to how much Ireland might receive.

Minister for Finance Michael Noonan welcomed the agreement but said: "[We have] ...a long way to go of course; and a lot of negotiations will have to be done; but if we had failed to get it in tonight - it would have been the end of the road. So we have kept our case going forward pretty strongly."

Enabling the €500bn rescue fund to shore up struggling banks directly is a pillar of Europe's so-called banking union, which seeks to hand European institutions the job of supervision and rescue rather than leaving weaker member states to fend for themselves.

"We have made an important step on the way to the banking union by agreeing on the main points for a future regime for direct bank recapitalisation," said German Finance Minister Wolfgang Schaeuble.

“We need the banking union to improve the trust of the financial markets in the stability of the European banking system," Mr Schaeuble said.

He and others cautioned, however, that despite a political agreement on the broad strokes, many operational details have yet to be hammered out.

The ESM's firepower to recapitalise banks will also be limited to €60bn to maintain the fund's top-notch credit rating, which it needs to raise money on the international bond markets.

Lending to banks that have lost market access is considered to be significantly riskier than lending to governments - for which it was initially set up as backstop - and so would hurt the ESM's credit rating.

They also gave final approval to a set of rules that requires EU banks to hold more capital to better withstand shocks from next year on.

The rules - the internationally agreed Basel III regulations - were adopted with a qualified majority. Only Britain voted against them since they were tied to a law that caps bonuses bankers can receive that London opposes.

In addition, the finance chiefs signed off on Latvia's bid to become the currency union's 18th member nation starting next year - a decision that will then have to be rubber-stamped by a summit of EU leaders next week.